Shape and Space 9

The diagram below shows a cuboid ABCDEFGH with AB = 4 cm, BC = 5 cm, and BF = 12 cm.

Work out the length of the space diagonal AE.

A pyramid has a square base PQRS, with PQ = QR = 6 cm. The vertex T is vertically above the centre of the base TSQ. The height VT = 9 cm.

Calculate the length of the edge VP from the vertex to a base corner.

A cuboid has dimensions 6 cm × 8 cm × 10 cm. Using Pythagoras’ theorem, explain how to find the length of its longest diagonal.

The diagram shows a rectangular box. The base AB = 9 cm, BC = 5 cm, and the height is BE = 12 cm. Point F is directly above C.

For a square-based pyramid with base edge of 10 cm and height of 15 cm (vertex directly above the centre), work out the vertical angle (angle between a side face and the base).

A right triangular prism has end triangle sides 3 cm, 4 cm and 5 cm, and height (length perpendicular to end) of 10 cm.

Calculate the length of the longest diagonal from one vertex to the opposite vertex on the other end.

In a solid with a rectangular base 7 cm × 10 cm, a point P is vertically above the centre of the base at a height of 12 cm. Explain how you would use trigonometry to find the angle between the edge from P to a base corner and the base plane.

The diagram shows a rectangular box (cuboid) with length 7 cm, width 5 cm and height 12 cm.

Calculate the length of the diagonal from point A to point G (opposite corners of the box). Give your answer correct to 3 significant figures.